Chapter 11 Investment. Net investment = increase in productive capital stock. I n t = K t K t-1. Investment. Intermediate Macroeconomics

Transcription

1 Chapter 11 Investment Investment 1. Introduction 2. Definitions 3. Model 1 Net present value (NPV) 4. Model 2 Simple accelerator 6. Model 4 Tobin s q 7. Complications 8. Policy Implications 1. Introduction Change in investment vs change in GDP 2. Definitions Net investment Change from previous year billions chained 1996 $ Real GDP Gross Investment Net investment = increase in productive capital stock I n t = K t K t-1 I n t = Net investment during period t K t = Capital stock at end of period t

2 2. Definitions Replacement investment and depreciation Replacement investment = spending necessary to maintain a constant productive capital stock I r t = d K t-1 I r t = investment in replacement capital in period t d = rate of depreciation, percent/year 2. Definitions Gross investment Gross investment = total spending on goods used to produce other goods and services I g t = In t + Ir t I g t = gross investment in period t 2. Definitions Gross and net investment Investment, percent of GDP 20% 15% 10% 5% 0% -5% -10% Gross Investment Net Investment Model 1 - Net Present Value (NPV) Present Value present day value of a future revenue or expense Present Value = cash flow year n (1 + i) n-1 i = nominal interest rate Net Present Value total present day value of all current and expected future revenues and expenses 2

3 3. Model 1 - Net Present Value (NPV) Case 1 Assume nominal interest rate = 10% = 0.10 All revenues and expenses occur at the beginning of the year. Revenue Expense Net Cash Flow NPV Year 1 $ 0 $100 - $100 - $100 Year Year Totals $130 $100 $30 $11.57 NPV = Year 1 Net + Year 2 Net + Year 3 Net i (1+i)( (1+i) 3. Model 1 - Net Present Value (NPV) Case 2 Year 3 revenue lowered from $80 to $60. Total revenue still exceeds total expense but NPV < $0. Assume nominal interest rate = 10% = 0.10 All revenues and expenses occur at the beginning of the year. Revenue Expense Net Cash Flow NPV Year 1 $ 0 $100 - $100 - $100 Year Year Totals $110 $100 $10 - $ 4.96 NPV = Year 1 Net + Year 2 Net + Year 3 Net i (1+i)( (1+i) 3. Model 1 - Net Present Value (NPV) Variables that affect investment Variables that affect investment: Demand (and income): increase in demand increases revenues and NPV of investment. Nominal interest rate: increase in interest rate reduces the NPV of future cash flows. If future net cash flows are positive, result is a lower NPV of investment. 4. Model 2 Simple Accelerator The desired level of capital stock is a fixed function of aggregate demand. K t = ß Y t K t-1 = ß Y t-1 K t-1 = stock of capital at end of period t-1 Y t = aggregate demand in period t 3

4 4. Model 2 Simple Accelerator Net investment Net investment equals the change in the level of capital stock. I n t = K t -K t-1 I n t = net investment in period t Firms instantaneously adjust the level of capital to the observed level of demand. I n t = ß Y t -ß Y t-1 = ß (Y t -Y t-1 ) 4. Model 2 - Simple Accelerator Variables that affect investment Variables that affect investment: Demand: increase in demand increases desired level of capital stock and investment. Desired net investment equals some fraction (ß) of the growth in demand. Desired gross investment equals some fraction of the growth in demand plus some fraction (d) of the beginning stock of capital. 5. Model 3 - Neoclassical Derive desired level of capital stock, K* Calculate investment as a function of: K* - K t-1 where, K* = desired level of capital K t-1 = stock of capital at start of the period t (end of preceding period, t-1) Desired stock of capital, K* Profit maximization problem Marginal product of capital Value of the marginal product of capital Rental (user) cost of capital Real interest rate and depreciation rate Nominal interest rate Expected inflation rate 4

5 Profit maximization Profit = p Y -c K -w L p = average product price Y = physical measure of output = production function, Y = f(k,l) c = rental (user) cost of capital K = available capital stock w = wage rate L = quantity of labor input Profit maximization Profit = p Y -c K -w L profit = p ( Y -c = 0 K K c = p ( Y K K* = f(p, c, w) p and w are observable, c is not observable Where Y = marginal product of capital K p Y = value of marginal product of capital K c = rental cost of capital K* = desired level of capital Rental cost of capital Real interest rate Rental cost equivalent to what it costs to buy capital today and then sell it one year from now. c* = r + d c* = rental cost of capital r = real interest rate d = depreciation rate r = i - E(B) r = real interest rate i = nominal interest rate E(B) = expected inflation rate 5

6 Nominal interest and inflation rates Nominal and real interest rates Percent per year 15 Nominal Interest Rate 10 5 Inflation Rate Interest Rate, percent per year Nominal Interest Rate Real Interest Rate Source: Nominal interest rate based on U.S. bank prime rate ( Inflation rate based on CPI measure of inflation ( Source: Nominal interest rate based on U.S. bank prime rate ( Real interest rate based on prime rate - CPI measure of inflation ( Expected inflation rate Naive expectations: E(B t ) = B t-1 Adaptive expectations: E(B t ) = E(B t-1 ) + a ( [B t-1 -E(B t-1 )] Rational expectations: E(B t ) = B t + random error Desired level of capital, K* Positive function of: Product price, p Product demand, Y Labor wage rate, w Negative function of Rental Cost of Capital, c c = r + d real interest rate (+), r = i E(B t ) + d nominal interest rate (+), i expected inflation rate (-), E expected depreciation rate (+), d 6

7 Flexible accelerator Adjustment of the capital stock How do you go from desired level of capital to investment? Flexible Accelerator Model - firms close a portion of the gap, a, between the desired and the current levels of capital I t = a ( (K* - K t-1 ) K* Capital Stock I t = 0.4 ( (K* - K t-1 ) Time 3. Model 3 Neoclassical Variables that affect investment Variables that affect investment: Demand (and income) (+) Product price (+) Wage rate (+) Real interest rate (-) Nominal interest rate (-) Expected inflation rate (+) 6. Tobin s q q = company s market value replacement cost of capital As the value of the stock market increases relative to the total stock of real capital then the rate of investment should increase. 7

8 7. Complications Credit Rationing unable to borrow money even for a good investment Capacity Utilization increase in demand does not motivate investment in existing capacity is underutilized. 8. Policy Implications Investment Tax Credits Temporary tax credit small impact on desired capital stock large impact on current period investment spending anti-recession policy Permanent tax credit larger impact on desired capital stock smaller impact on current period investment spending long-run growth policy 8. Policy Implications Corporate Income Tax 8. Policy Implications Corporate Income Tax Is investment financed from borrowed funds or equity funds (e.g., stock sale)? Borrowed Funds - interest payments on borrowed funds deducted from firm s income before income tax calculated. Equity Funds - interest payments (e.g. dividends) on funds are not deducted from firm s income before tax is calculated. Borrowed Funds + Product sales - Raw materials & labor -Depreciation - Interest payments on borrowed funds Gross Profit - Corporate income tax Net Profit Equity Funds + Product sales - Raw materials & labor -Depreciation Gross Profit - Corporate income tax Net Profit - Dividends on equity funds 8